Gray Molasses Cooling of Lithium-6 Towards a Degenerate Fermi Gas

Department of Physics and Astronomy University of Heidelberg Master thesis in Physics submitted by Manuel Gerken born in Frankfurt am Main 2016 Gray Molasses Cooling of Lithium-6 Towards a Degenerate Fermi Gas This Master thesis has been carried out by Manuel Gerken at the Physikalisches Institut Heidelberg under the supervision of Prof. Dr. Matthias Weidemüller iv Kühlen mit grauer Melasse zur Realisierung eines entarteten Fermi Gases Die vorliegende Arbeit beschreibt das Design, die Implementierung und die Charakteri- sierung einer Kühlung in grauer Melasse auf der D1 Linie von Lithium-6 Atomen. Durch diese zusätzliche Laser-Kühlung erreichen wir sub-Doppler Temperaturen für eine an- fänglich magneto-optisch gefangenes Gas und erhöhen seine Phasenraumdichte um einen Faktor von etwa 10. Kühlen mit grauer Melasse kombiniert die geschwindigkeitsabhängige Besetzung eines kohärenten Dunkelzustands mit einem sisyphusartigen Kühlprozess auf einer ortsabhän- gigen Energieverschiebung. Wir präsentieren Berechnungen und Analysen von bekleide- ten Energiezuständen von Lithium-6 in ein- und dreidimensionalen Polarisationsgradien- tenfeldern. Dieser erzeugen die ortsabhängige Energieverschiebung für die Kühlung mit grauer Melasse. Wir beschreiben die Planung und den Aufbau des Experiments, in dem 3.2×107 Atome innerhalb von 1 ms von 240 µK auf 42 µK herabgekühlt werden. Dies ent- spricht einer Einfangeffizienz von 80% gegenüber der anfangs in der magneto-optischen Falle hergestellten Probe. Wir messen die Auswirkungen von Frequenzverstimmung, Dau- er, Magnetfeld und Lichtintensitäten auf den Kühlprozess um optimale Parameter zu er- halten. Wir diskutieren, wie die erhöhte Phasenraumdichte die Übertragungseffizienz in die optische Dipolfalle verbessert. Die verbesserten Ausgangsbedingungen für evaporati- ves Kühlen ermöglichen es uns, ein stark entartetes Fermigas herzustellen, der Grundbau- stein für die Generierung einer suprafluiden Bose-Fermi-Mischung und die Untersuchung von Fermi Polaronen. Gray Molasses Cooling of Lithium-6 Towards a Degenerate Fermi Gas This thesis presents the design, implementation and characterization of gray molasses cooling on the D1 line of Lithium-6 atoms. With this approach we reach sub-Doppler temperatures for an initially magneto-optically trapped gas and increase its phase space density by a factor of approximately 10. Gray molasses cooling consists of a velocity-selective coherent population trapping of atoms at zero velocity in a dark state that works in combination with a Sisyphus-like cooling process in a spatially dependent light-shift. We present calculations and analysis of dressed state energies of Lithium-6 in one and three dimensional polarization gradient fields, which generate the spatially dependent energy shift of the gray molasses cooling. Design and setup for the experiment are described, in which 3.2 × 107 atoms are cooled from 240 µK to 42 µK in 1 ms. The atom number represents an 80% capture efficiency of the initial sample prepared in the magneto-optical trap. We measure and optimize the impact of frequency detuning, duration, magnetic field and beam intensities onto the cooling process. We discuss how the increased phase space density will improve the transfer efficiency into the optical dipole trap. The enhanced starting conditions for forced evaporative cooling will enable us to achieve a highly degenerate Fermi gas, the keystone to a double superfluid Bose-Fermi mixture and the investigation of Fermi polarons. v Contents 1 Introduction 1 2 Concept of gray molasses cooling 5 2.1 Principle of gray molasses cooling ................... 5 2.2 Λ configuration and coherent dark state ................ 7 2.3 Polarization gradient fields ....................... 9 2.4 Gray molasses of Lithium-6 ...................... 12 2.5 Calculations for Lithium-6 in gray molasses .............. 15 2.5.1 Description of light polarization ................ 15 2.5.2 Hamiltonian describing gray molasses ............. 17 2.5.3 Discussion of gray molasses in 1D Lin⊥Lin field ....... 20 2.5.4 Discussion of gray molasses in a 3D σ+-σ− field ....... 24 3 Implementation of gray molasses cooling of Lithium-6 27 3.1 Setup of the gray molasses ....................... 27 3.1.1 Laser system and stabilization ................. 28 3.1.2 Optical setup for light preparation .............. 30 3.1.3 Optical setup at experimental chamber ............ 32 3.2 Characterization of gray molasses cooling ............... 33 3.2.1 Experimental sequence ..................... 33 3.2.2 Measurements of gray molasses cooling ............ 35 4 Conclusion and further developments 45 Bibliography 53 Acknowledgment 63 vii 1 Introduction Ultracold atomic gases yield an advantageous environment for the probing and simulation of few and many-body physics (Bloch et al., 2008). The features of controlling internal degrees of freedom, external motional states, the density of the gas, the potential shape and even the atomic interactions, of a cloud of atoms or a mixture of atoms, makes the field feasible for the investigation of a wide range of physical questions. One example is the simulation of magnetic spins in a condensed matter system where the interaction between the spins is of a long- range nature and spatially anisotropic. Such a system can be simulated with an ultracold gas of polar molecules where the strength of the electric dipole-dipole interaction can be controlled to uttermost accuracy (Pupillo et al., 2008; Quéméner and Julienne, 2012). Another example are Fermi impurities interacting with a degenerate Bose environment. This system simulates electrons moving in a lattice of positively charged atoms in a crystal. The interaction between the electron and the environment leads to a quasi-particle called "Fröhlich-polaron" with a different mass and energy compared to the bare electron (Fröhlich, 1954; Tempere et al., 2009). The last example is the generation of a double superfluid phase of a Bose- Fermi mixture. The historical approach to achieve this phase using Helium-4 and Helium-3 reaches a limit when decreasing the temperature. The density of Helium-4 drops to zero before Helium-3 reaches superfluidity (Edwards, 2013). Such a system can be simulated using ultracolt atomic gases. All of these three examples can be studied in an ultracold Bose-Fermi mixture of Cesium-133 and Lithium-6 under favorable conditions. A polar molecule of Cesium- 133 and Lithium-6 holds the strongest electric dipole moment in the singlet ground state of all alkali combinations leading to enhanced interaction effects (Aymar and Dulieu, 2005). The high mass ratio of Cesium-133 and Lithium-6 of 22.1:1 leads to simplifications in the theoretic description for Fermi polarons and double superfluidity. Theories for static polarons, in the limit of infinitely heavy impurities, can directly be tested in the case of Cesium-133 impurities immersed in a Lithium-6 1 Chapter 1. Introduction Fermi sea. The mass ratio is predicted to change the interaction energy between the two superfluids (Zhang et al., 2014). The study of all these fundamental properties of a strongly interaction Bose-Fermi gas will benefit from a favorable scattering resonances between Lithium-6 and Cesium-133, leading to controllable intra and inter species interactions (Tung et al., 2013; Repp et al., 2013; Pires et al., 2014; Ulmanis et al., 2015). A long journey of progress in technical and physical understandings of 40 years lead to the point where we can address these questions in ultracold atomic systems. The proposal by Hänsch and Schawlow (1975) to cool a vapor of atoms by intense quasi-monochromatic laser light in 1975 was the beginning of laser cooling, a milestone in ultracold atomic physics. In the following years laser cooling and trapping methods were developed and awarded with the Nobel Prize in 1997 (Phillips, 1998; Chu, 1998; Cohen-Tannoudji, 1998). The realization of Bose-Einstein condensation (BEC) in diluted atomic gases in 1995 (Davis et al., 1995; Bradley et al., 1995; An- derson et al., 1995) was the first experimental generation of a degenerate quantum gas and was honored with the Nobel prize in 2001 (Cornell and Wieman, 2002; Ketterle, 2002). Due to the ultralow temperature, a dilute Bose gas with a phase space density of approximately one can be produced. In such a gas a macroscopic part of the ensemble occupies the lowest energy state of the system. This leads to a macroscopic quantum wavefunction. A few years after the generation of BEC the first degenerate Fermi gas was realized by laser cooled atoms (DeMarco and Jin, 1999; Schreck et al., 2001; Truscott et al., 2001; Hadzibabic et al., 2002). The discovery of magnetic Feshbach resonances in 1998 marked another milestone in the field of ultracold atomic physics (Inouye et al., 1998; Courteille et al., 1998). Such scattering resonances allow to control and tune the complete scattering process at ultracold temperatures, where it is described by the s-wave scattering length a. This ability of tuning the interaction between two different atoms or two spin components of the same atomic species opened the door for the observation of many new effects. The first realization of a BEC out of weakly bound molecules (a > 0), formed from two fermionic components, was achieved in 2003 (Jochim et al., 2003; Zwierlein et al., 2003; Greiner et al., 2003). For weakly attractive interactions (a < 0) pairing mechanism of a two component Fermi gas could be investigated (Chin et al., 2004; Schunck et al., 2008). This mechanism describes low temperature superconductivity and was predicted by the Bardeen-Cooper-Schrieffer theory (BCS) (Bardeen et al., 1957). 2 Ultracold gases with tunable interactions have been applied to address polaron physics and double superfluidity. Attractive and repulsive Fermi polarons have been detected for impurities in a highly degenerate, single-species fermionic sample by changing the internal state of the impurity from a non-interacting into an interacting state while tuning the interactions between bath and impurity using Feshbach resonances (Schirotzek et al., 2009; Kohstall et al., 2012; Koschorreck et al., 2012). In 2016 ultrafast dynamics of impurities immersed in a single species Fermi sea were investigated (Cetina et al., 2016).

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